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A Paper-Tire is a virtual product defined as a set of force and moment equations that are entirely determined by well defined and widely recognized tire characteristics (such as cornering stiffness, peak location, and slide/peak ratio). The vehicle dynamicist may use the Paper-Tire concept to study the effects of tires with various hypothetical characteristics on vehicle behavior. If the dynamicist discovers a set of characteristics yielding a desired vehicle response, he could then ask tire manufacturers to attempt to develop a tire specification with the preferred characteristics. (There is, of course, no guarantee that tire manufacturers can develop a practical tire with the preferred characteristics.) The paper explains the general principles of the Paper-Tire concept with the help of the BNPS model (derived from the ‘Magic Formula’). A limited set of examples for tire cornering and braking performance are provided at a single load; further possible developments are indicated.

The objective was derivation of a tire braking/cornering force model based on only a few standard tests, so that elaborate testing of all possible combinations of lateral and longitudinal forces could be avoided Such a model would be particularly useful for truck and bus tires because testing large tires is expensive and appropriate testing facilities are rare The required model can be derived from the concept of the slip circle (not a friction force circle) Using the slip circle concept, all tire forces at any cornering/braking combination can be predicted from the results of only two basic tests -- a free-rolling cornering test and straight-line braking test The slip circle concept has been incorporated into a subroutine called the COMBINATOR -- a piece of public domain software sponsored by SAE Cooperative Research This paper discusses the Slip Circle Model, introduces the COMBINATOR, and demonstrates effectiveness by comparison of modeling results and experimental data

The “Magic Formula” concept is an elegant, empirical method of fitting tire data for inclusion in vehicle dynamics models. Its behavior as a function of parameter values is explained in detail in this paper. This paper presents the BNPS model, a modification of the Magic Formula concept, which has been fully automated on a personal computer. This allows the ready reduction of data into practical Magic Formula type models without any investment of engineering time. BNPS fitting example results are presented.